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MIT OpenCourseWareMIT 18.03 Differential Equations, Spring 2006 (2006)

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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.


This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Audio/Visual: sound, color
Language: English
Keywords: Ordinary Differential Equations, ODE, modeling physical systems, first-order ODE's, Linear ODE's, second order ODE's, second order ODE's with constant coefficients, Undetermined coefficients, variation of parameters, Sinusoidal signals, exponential signals, oscillations, damping, resonance, Complex numbers and exponentials, Fourier series, periodic solutions, Delta functions, convolution, Laplace transform methods Matrix systems, first order linear systems, eigenvalues and eigenvectors, Non-linear autonomous systems, critical point analysis, phase plane diagrams

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0 United States


Individual Files

Movie Files MPEG4 Ogg Video Real Media
Lec 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves. 103.9 MB
203.1 MB
Lec 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves. 77.7 MB
Lec 10: Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations. 98.3 MB
192.0 MB
Lec 10: Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations. 73.8 MB
Lec 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. 105.9 MB
209.1 MB
Lec 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. 80.4 MB
Lec 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's. 97.8 MB
191.8 MB
Lec 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's. 73.7 MB
Lec 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials. 93.5 MB
196.9 MB
Lec 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials. 76.2 MB
Lec 14: Interpretation of the Exceptional Case: Resonance. 102.0 MB
184.9 MB
Lec 14: Interpretation of the Exceptional Case: Resonance. 70.6 MB
Lec 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi). 112.5 MB
204.7 MB
Lec 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi). 78.8 MB
Lec 16: Continuation: More General Periods; Even and Odd Functions; Periodic Extension. 99.9 MB
204.3 MB
Lec 16: Continuation: More General Periods; Even and Odd Functions; Periodic Extension. 78.6 MB
Lec 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds. 94.8 MB
188.9 MB
Lec 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds. 72.7 MB
Lec 19: Introduction to the Laplace Transform; Basic Formulas. 90.5 MB
196.0 MB
Lec 19: Introduction to the Laplace Transform; Basic Formulas. 75.9 MB
Lec 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations. 120.1 MB
211.6 MB
Lec 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations. 80.7 MB
Lec 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's. 98.1 MB
208.5 MB
Lec 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's. 81.2 MB
Lec 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. 81.8 MB
180.7 MB
Lec 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. 70.5 MB
Lec 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs. 83.4 MB
179.6 MB
Lec 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs. 70.1 MB
Lec 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions. 93.1 MB
185.4 MB
Lec 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions. 71.4 MB
Lec 24: Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. 89.8 MB
192.8 MB
Lec 24: Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. 74.7 MB
Lec 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). 96.4 MB
200.2 MB
Lec 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). 78.1 MB
Lec 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues. 97.5 MB
191.1 MB
Lec 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues. 74.1 MB
Lec 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients. 110.4 MB
208.0 MB
Lec 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients. 80.1 MB
Lec 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. 104.8 MB
194.2 MB
Lec 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. 74.5 MB
Lec 29: Matrix Exponentials; Application to Solving Systems. 97.2 MB
200.6 MB
Lec 29: Matrix Exponentials; Application to Solving Systems. 77.8 MB
Lec 3: Solving First-order Linear ODE's; Steady-state and Transient Solutions. 108.3 MB
207.5 MB
Lec 3: Solving First-order Linear ODE's; Steady-state and Transient Solutions. 80.2 MB
Lec 30: Decoupling Linear Systems with Constant Coefficients. 111.7 MB
194.5 MB
Lec 30: Decoupling Linear Systems with Constant Coefficients. 74.8 MB
Lec 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum. 94.8 MB
189.8 MB
Lec 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum. 75.2 MB
Lec 32: Limit Cycles: Existence and Non-existence Criteria. 94.6 MB
187.7 MB
Lec 32: Limit Cycles: Existence and Non-existence Criteria. 72.9 MB
Lec 33: Relation Between Non-linear Systems and First-order ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle. 91.4 MB
203.5 MB
Lec 33: Relation Between Non-linear Systems and First-order ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle. 79.8 MB
Lec 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's. 108.9 MB
208.4 MB
Lec 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's. 79.8 MB
Lec 5: First-order Autonomous ODE's: Qualitative Methods, Applications. 98.5 MB
189.9 MB
Lec 5: First-order Autonomous ODE's: Qualitative Methods, Applications. 72.8 MB
Lec 6: Complex Numbers and Complex Exponentials. 95.7 MB
188.2 MB
Lec 6: Complex Numbers and Complex Exponentials. 72.2 MB
Lec 7: First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. 89.6 MB
170.0 MB
Lec 7: First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. 65.4 MB
Lec 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models. 111.5 MB
210.3 MB
Lec 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models. 80.3 MB
Lec 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases. 108.8 MB
208.0 MB
Lec 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases. 79.5 MB
Image Files Thumbnail Animated GIF
Lec 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves. 5.6 KB
437.3 KB
Lec 10: Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations. 5.9 KB
433.3 KB
Lec 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. 5.9 KB
430.0 KB
Lec 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's. 4.7 KB
436.2 KB
Lec 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials. 5.8 KB
425.7 KB
Lec 14: Interpretation of the Exceptional Case: Resonance. 6.9 KB
440.0 KB
Lec 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi). 5.8 KB
436.5 KB
Lec 16: Continuation: More General Periods; Even and Odd Functions; Periodic Extension. 5.7 KB
433.5 KB
Lec 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds. 5.1 KB
442.5 KB
Lec 19: Introduction to the Laplace Transform; Basic Formulas. 5.2 KB
421.2 KB
Lec 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations. 6.8 KB
437.2 KB
Lec 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's. 5.7 KB
429.3 KB
Lec 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. 6.5 KB
424.9 KB
Lec 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs. 5.6 KB
425.9 KB
Lec 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions. 5.3 KB
433.8 KB
Lec 24: Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. 5.3 KB
428.9 KB
Lec 25: Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). 5.9 KB
434.6 KB
Lec 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues. 6.2 KB
433.7 KB
Lec 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients. 5.4 KB
427.9 KB
Lec 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. 5.5 KB
431.4 KB
Lec 29: Matrix Exponentials; Application to Solving Systems. 6.1 KB
439.6 KB
Lec 3: Solving First-order Linear ODE's; Steady-state and Transient Solutions. 4.7 KB
440.6 KB
Lec 30: Decoupling Linear Systems with Constant Coefficients. 5.4 KB
432.3 KB
Lec 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum. 6.0 KB
443.2 KB
Lec 32: Limit Cycles: Existence and Non-existence Criteria. 5.2 KB
442.9 KB
Lec 33: Relation Between Non-linear Systems and First-order ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle. 4.7 KB
433.7 KB
Lec 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's. 6.2 KB
434.4 KB
Lec 5: First-order Autonomous ODE's: Qualitative Methods, Applications. 6.3 KB
443.1 KB
Lec 6: Complex Numbers and Complex Exponentials. 5.5 KB
414.0 KB
Lec 7: First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. 7.0 KB
434.6 KB
Lec 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models. 5.5 KB
430.2 KB
Lec 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases. 5.5 KB
433.0 KB
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MIT18.03S06_files.xml Metadata [file]
MIT18.03S06_meta.xml Metadata 2.1 KB
MIT18.03S06_reviews.xml Metadata 657.0 B

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Reviewer: YajurTheJ - 4.00 out of 5 stars4.00 out of 5 stars4.00 out of 5 stars4.00 out of 5 stars - April 2, 2012
Subject: A Word of Thanks!
I found the video lectures extremely useful in understanding about differential equations. These videos helps me improving my DE skills to a much higher level, studied along with rest of the material in MIT OCW. Great thing!!!